(1) will write us of the following form
[tex]\dfrac{dy}{dx}+y^2\sin x=0\\ \\
[/tex]
(2) [do not it need explanation]
[tex]\dfrac{dy}{dx}=-y^2\sin x\\ \\
[/tex]
(3) Left place variable "y" and right place, variable "x" like this
[tex]\dfrac{dy}{y^2}=-\sin x\, dx\\ \\[/tex]
(4) Integrate both members
[tex]\displaystyle
\int \dfrac{dy}{y^2}=\int-\sin x\, dx\\ \\[/tex]
(5) Solve us the integrals
[tex]-\dfrac{1}{y}= \cos x+C[/tex]
(6) Isolate variable "y"
[tex]\boxed{y=-\dfrac{1}{\cos x+C}}[/tex]
C: any cosntant
